LaTeX Modes

When LaTeX is processing your input text, it is always in one of three
modes:

Paragraph mode

Math mode

Left-to-right mode, called LR mode for short

LaTeX changes mode only when it goes up or down a staircase to a
different level, though not all level changes produce mode changes.
Mode changes occur only when entering or leaving an environment, or
when LaTeX is processing the argument of certain text-producing
commands.

Paragraph mode is the most common; it's the one LaTeX is in
when processing ordinary text. In that mode, LaTeX breaks your text
into lines and breaks the lines into pages. LaTeX is in math
mode
when it's generating a mathematical formula. In LR mode, as in
paragraph mode, LaTeX considers the output that it produces to be a
string of words with spaces between them. However, unlike paragraph
mode, LaTeX keeps going from left to right; it never starts a new line in
LR mode. Even if you put a hundred words into an \mbox, LaTeX would
keep typesetting them from left to right inside a single box, and
then complain because the resulting box was too wide to fit on the line.

LaTeX is in LR mode when it starts making a box with an \mbox command.
You can get it to enter a different mode inside the box - for example,
you can make it enter math mode to put a formula in the box. There
are also several text-producing commands and environments for making a
box that put LaTeX in paragraph mode. The box make by one of these
commands or environments will be called a parbox. When LaTeX is in
paragraph mode while making a box, it is said to be in inner paragraph
mode. Its normal paragraph mode, which it starts out in, is called
outer paragraph mode.